Método estadístico que analiza simultáneamente múltiples características en cada muestra objeto de estudio.
Algunos ejemplos:
Análisis de componentes principales
Análisis de correspondencias
Escalamiento multidimensional
Análisis de correspondencias canónico
Etc.
Análisis de componentes principales (PCA)
El objetivo es reducir un gran número de variables perdiendo la menor cantidad de información posible.
Los nuevos componentes principales o factores serán una combinación lineal de las variables originales e independientes entre sí.
La interpretación de los factores se deducirá observando su relación con las variables iniciales.
Fases:
Análisis de la matriz de correlaciones. Deben existir altas correlaciones entre las variables.
Selección de los factores. El primer factor recoje la mayor proporción de variabilidad original, el segundo, la máxima no recogida por el primero, etc.
Análisis de la matriz factorial. Se representan los factores seleccionados en forma de matriz.
Interpretación de los factores
Ejemplo modelización riqueza plantas exóticas a partir del clima
Modelar riqueza de especies exóticas utilizando variables climáticas.
library(visreg)par(mfcol=c(1,2))visreg(glm_exoticas2, scale="response", ylab="Riqueza de especies")
Escalamiento multidimensional no métrico (NMDS)
Representación de las distancias existentes entre un conjunto de datos en un espacio geométrico de pocas dimensiones.
1. Cálculo matriz de disimilaridad X a partir de la matriz de datos.
2. Asignación de unidades muestrales a una configuración inicial aleatoria
3. Cálculo distancias otra vez en este nuevo espacio geométrico y se calcula una matriz de distancia Y
4. Se comparan las matrices de distancia X e Y y se miden cómo son de parecidas entre ellas (stress)
5. A partir de la configuración inicial, se reasignan las unidades muestrales para reducir las distancia con la matriz X
6. Repetición iterativa del proceso hasta que se consigue una solución óptima (se minimiza el stress)
Gradiente de composición florística en bosques tropicales montanos
Investigar qué variables ambientales afectan a la composición florística de árboles en distintos tipos de bosques tropicales. Abundancia de cada especie en cada parcela.
1. Explorar visualmente cómo son de similares las parcelas muestreadas en función de la composición de especies
2. Investigar relación de esta ordenación y las variables ambientales.
bio <-read.table("MANOVA-bio.txt", header=T, sep="\t")env <-read.table("MANOVA-env.txt", header=T, sep="\t")
Square root transformation
Wisconsin double standardization
Run 0 stress 0.1813191
Run 1 stress 0.189724
Run 2 stress 0.1914815
Run 3 stress 0.1827766
Run 4 stress 0.1888635
Run 5 stress 0.1762361
... New best solution
... Procrustes: rmse 0.01048257 max resid 0.1464194
Run 6 stress 0.1927798
Run 7 stress 0.1969669
Run 8 stress 0.1814796
Run 9 stress 0.1762361
... New best solution
... Procrustes: rmse 0.000678957 max resid 0.008967172
... Similar to previous best
Run 10 stress 0.176237
... Procrustes: rmse 0.0008545313 max resid 0.01134997
Run 11 stress 0.2003403
Run 12 stress 0.1867425
Run 13 stress 0.1871088
Run 14 stress 0.1810092
Run 15 stress 0.1876214
Run 16 stress 0.1806629
Run 17 stress 0.1930107
Run 18 stress 0.1762369
... Procrustes: rmse 0.0002173221 max resid 0.002312363
... Similar to previous best
Run 19 stress 0.1841313
Run 20 stress 0.1762357
... New best solution
... Procrustes: rmse 8.135117e-05 max resid 0.0010794
... Similar to previous best
Run 21 stress 0.1900143
Run 22 stress 0.1868287
Run 23 stress 0.1907046
Run 24 stress 0.186743
Run 25 stress 0.1762374
... Procrustes: rmse 0.0002461696 max resid 0.002268407
... Similar to previous best
Run 26 stress 0.1969186
Run 27 stress 0.1762361
... Procrustes: rmse 0.000557169 max resid 0.007301201
... Similar to previous best
Run 28 stress 0.1867422
Run 29 stress 0.1797416
Run 30 stress 0.1867433
Run 31 stress 0.1784679
Run 32 stress 0.1907052
Run 33 stress 0.1828305
Run 34 stress 0.1868239
Run 35 stress 0.1900136
Run 36 stress 0.1784677
Run 37 stress 0.1881263
Run 38 stress 0.1900146
Run 39 stress 0.1812821
Run 40 stress 0.18148
Run 41 stress 0.1762366
... Procrustes: rmse 0.0007213377 max resid 0.009669698
... Similar to previous best
Run 42 stress 0.2091809
Run 43 stress 0.1841312
Run 44 stress 0.1812541
Run 45 stress 0.1806618
Run 46 stress 0.1846137
Run 47 stress 0.1925728
Run 48 stress 0.2017255
Run 49 stress 0.1868236
Run 50 stress 0.1793479
Run 51 stress 0.1762362
... Procrustes: rmse 0.0006659768 max resid 0.00892909
... Similar to previous best
Run 52 stress 0.2041754
Run 53 stress 0.176236
... Procrustes: rmse 0.0005829137 max resid 0.007660708
... Similar to previous best
Run 54 stress 0.1762371
... Procrustes: rmse 0.0001766661 max resid 0.001593336
... Similar to previous best
Run 55 stress 0.201832
Run 56 stress 0.188662
Run 57 stress 0.1762368
... Procrustes: rmse 0.0005127457 max resid 0.00592756
... Similar to previous best
Run 58 stress 0.1868218
Run 59 stress 0.1762354
... New best solution
... Procrustes: rmse 0.0003546211 max resid 0.004754731
... Similar to previous best
Run 60 stress 0.1793475
Run 61 stress 0.1961999
Run 62 stress 0.1841311
Run 63 stress 0.1905914
Run 64 stress 0.1955569
Run 65 stress 0.1762375
... Procrustes: rmse 0.0005533177 max resid 0.007094434
... Similar to previous best
Run 66 stress 0.1873162
Run 67 stress 0.1762353
... New best solution
... Procrustes: rmse 6.371811e-05 max resid 0.0008595397
... Similar to previous best
Run 68 stress 0.1841318
Run 69 stress 0.1762367
... Procrustes: rmse 0.0002742295 max resid 0.002257947
... Similar to previous best
Run 70 stress 0.1809903
Run 71 stress 0.1806618
Run 72 stress 0.2070922
Run 73 stress 0.1848277
Run 74 stress 0.1762355
... Procrustes: rmse 0.0002205998 max resid 0.002960223
... Similar to previous best
Run 75 stress 0.1940907
Run 76 stress 0.1793489
Run 77 stress 0.1762366
... Procrustes: rmse 0.0003673795 max resid 0.004916036
... Similar to previous best
Run 78 stress 0.1846118
Run 79 stress 0.1811326
Run 80 stress 0.1762382
... Procrustes: rmse 0.0003724917 max resid 0.002683883
... Similar to previous best
Run 81 stress 0.1762357
... Procrustes: rmse 0.0003326045 max resid 0.004462617
... Similar to previous best
Run 82 stress 0.1762363
... Procrustes: rmse 0.0003420567 max resid 0.004310418
... Similar to previous best
Run 83 stress 0.1797412
Run 84 stress 0.1762378
... Procrustes: rmse 0.0004579141 max resid 0.005689723
... Similar to previous best
Run 85 stress 0.1827383
Run 86 stress 0.1806621
Run 87 stress 0.1868278
Run 88 stress 0.1762366
... Procrustes: rmse 0.0003862705 max resid 0.004936148
... Similar to previous best
Run 89 stress 0.1788668
Run 90 stress 0.1952555
Run 91 stress 0.1806617
Run 92 stress 0.194699
Run 93 stress 0.176236
... Procrustes: rmse 0.0002694521 max resid 0.003259305
... Similar to previous best
Run 94 stress 0.1882663
Run 95 stress 0.1784668
Run 96 stress 0.1861735
Run 97 stress 0.1784682
Run 98 stress 0.184131
Run 99 stress 0.184829
Run 100 stress 0.1827756
Run 101 stress 0.1841308
Run 102 stress 0.1861665
Run 103 stress 0.1827755
Run 104 stress 0.1762367
... Procrustes: rmse 0.0003568748 max resid 0.004308465
... Similar to previous best
Run 105 stress 0.2006077
Run 106 stress 0.1814799
Run 107 stress 0.1784683
Run 108 stress 0.1793487
Run 109 stress 0.1784685
Run 110 stress 0.1762358
... Procrustes: rmse 0.0002237247 max resid 0.002995317
... Similar to previous best
Run 111 stress 0.1784679
Run 112 stress 0.1868273
Run 113 stress 0.1881279
Run 114 stress 0.2025052
Run 115 stress 0.2076421
Run 116 stress 0.2014525
Run 117 stress 0.20537
Run 118 stress 0.1815359
Run 119 stress 0.1841231
Run 120 stress 0.1868274
Run 121 stress 0.1861735
Run 122 stress 0.1876213
Run 123 stress 0.1868278
Run 124 stress 0.1814789
Run 125 stress 0.1841231
Run 126 stress 0.1784673
Run 127 stress 0.1856853
Run 128 stress 0.1784671
Run 129 stress 0.176237
... Procrustes: rmse 0.0004403699 max resid 0.005373281
... Similar to previous best
Run 130 stress 0.2017536
Run 131 stress 0.1812534
Run 132 stress 0.1881266
Run 133 stress 0.1813021
Run 134 stress 0.178467
Run 135 stress 0.1762371
... Procrustes: rmse 0.0004431638 max resid 0.004958917
... Similar to previous best
Run 136 stress 0.1980442
Run 137 stress 0.1784665
Run 138 stress 0.1867407
Run 139 stress 0.1784666
Run 140 stress 0.1793485
Run 141 stress 0.1881263
Run 142 stress 0.1857336
Run 143 stress 0.2084805
Run 144 stress 0.1762355
... Procrustes: rmse 0.0001216775 max resid 0.001623193
... Similar to previous best
Run 145 stress 0.1793475
Run 146 stress 0.1762368
... Procrustes: rmse 0.0004021772 max resid 0.005153592
... Similar to previous best
Run 147 stress 0.1827755
Run 148 stress 0.1891872
Run 149 stress 0.1827755
Run 150 stress 0.1762373
... Procrustes: rmse 0.000497628 max resid 0.006287264
... Similar to previous best
Run 151 stress 0.1867423
Run 152 stress 0.1841322
Run 153 stress 0.1814788
Run 154 stress 0.1846855
Run 155 stress 0.1793477
Run 156 stress 0.1784684
Run 157 stress 0.1788671
Run 158 stress 0.1814783
Run 159 stress 0.1762377
... Procrustes: rmse 0.000558887 max resid 0.007072896
... Similar to previous best
Run 160 stress 0.1908243
Run 161 stress 0.1794581
Run 162 stress 0.1793476
Run 163 stress 0.1784678
Run 164 stress 0.1841305
Run 165 stress 0.1762359
... Procrustes: rmse 0.0002694401 max resid 0.003608414
... Similar to previous best
Run 166 stress 0.1762358
... Procrustes: rmse 0.0003455068 max resid 0.004633095
... Similar to previous best
Run 167 stress 0.1938621
Run 168 stress 0.2059901
Run 169 stress 0.201116
Run 170 stress 0.1788661
Run 171 stress 0.181282
Run 172 stress 0.1827772
Run 173 stress 0.1841227
Run 174 stress 0.1924749
Run 175 stress 0.1805974
Run 176 stress 0.1762356
... Procrustes: rmse 0.000280365 max resid 0.003762712
... Similar to previous best
Run 177 stress 0.1762367
... Procrustes: rmse 0.000397959 max resid 0.005328579
... Similar to previous best
Run 178 stress 0.1762363
... Procrustes: rmse 0.0003092645 max resid 0.003841927
... Similar to previous best
Run 179 stress 0.1867429
Run 180 stress 0.1762356
... Procrustes: rmse 0.0001598903 max resid 0.001479898
... Similar to previous best
Run 181 stress 0.1876923
Run 182 stress 0.1827756
Run 183 stress 0.1762355
... Procrustes: rmse 0.0001304249 max resid 0.001747588
... Similar to previous best
Run 184 stress 0.1762369
... Procrustes: rmse 0.0004370817 max resid 0.00564469
... Similar to previous best
Run 185 stress 0.2036807
Run 186 stress 0.1841236
Run 187 stress 0.1821859
Run 188 stress 0.1762366
... Procrustes: rmse 0.0003872861 max resid 0.00494709
... Similar to previous best
Run 189 stress 0.1762364
... Procrustes: rmse 0.0003462769 max resid 0.004370201
... Similar to previous best
Run 190 stress 0.1881265
Run 191 stress 0.1762381
... Procrustes: rmse 0.0003599562 max resid 0.002512741
... Similar to previous best
Run 192 stress 0.2003486
Run 193 stress 0.1762357
... Procrustes: rmse 0.0003177059 max resid 0.004263728
... Similar to previous best
Run 194 stress 0.2015027
Run 195 stress 0.1861732
Run 196 stress 0.1881268
Run 197 stress 0.2029969
Run 198 stress 0.1793489
Run 199 stress 0.1762372
... Procrustes: rmse 0.0003698368 max resid 0.004101882
... Similar to previous best
Run 200 stress 0.1876549
*** Best solution repeated 31 times
plot(nmds_1)
Gráfico con diferencias por tipo de bosque y relación lineal con variables